Vol. 11, No. 2, 2018

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Zero divisor graphs of commutative graded rings

Katherine Cooper and Brian Johnson

Vol. 11 (2018), No. 2, 283–295
Abstract

We study a natural generalization of the zero divisor graph introduced by Anderson and Livingston to commutative rings graded by abelian groups, considering only homogeneous zero divisors. We develop a basic theory for graded zero divisor graphs and present many examples. Finally, we examine classes of graphs that are realizable as graded zero divisor graphs and close with some open questions.

Keywords
graded ring, zero divisor graph
Mathematical Subject Classification 2010
Primary: 05C25, 13A02
Milestones
Received: 30 September 2016
Revised: 17 March 2017
Accepted: 23 March 2017
Published: 17 September 2017

Communicated by Scott T. Chapman
Authors
Katherine Cooper
Department of Mathematics
University of Kentucky
Lexington, KY
United States
Brian Johnson
Department of Mathematics
Florida Gulf Coast University
Fort Myers, FL
United States